I’m by no means an expert but I’ll give it a shoot answering.
The reason your NES zapper works and not your PSX gun is that they work in different ways, my guess is that your TV does some re-modulation of the signal to give you the higher resolution and that messes with the PSX gun that needs very specific timings etc.
The NES zapper and duck hunt works by basically turning the screen black for a frame then a frame that’s mostly black but lights the position of the duck, the zapper is “stupid” in the fact that it doesn’t really care where you point it, it just looks for a light. If you shine a light in to the zapper you basically hit every time no matter where you point it.
The OSX gun is a bit more complex, the yellow connector is just a tap on your composite signal and that’s because PlayStation uses sync on composite, meaning the gun listens to the sync to get the H-sync which is much faster than V-sync and therefor more accurate.
Add to that that you actually calibrate the gun, probably to calibrate the sync to your specific TV since not all CRT screens are created equal due to the more fast paced syncing.
The TV then as I understand it (might be wrong) draw one black frame and run a dot over it, the gun registers the dot and figures out with the help of the sync where exactly you are pointing your gun, therefor just shining a light in the GunCon will make the gun think you are just shooting the left most corner.
So my guess earlier about your TV doing some fancy thing to give you that nice resolution also messes with the H-sync meaning your gun might not work or work sporadically while the duck zapper being much simpler works just fine, as to what OSSC can do to help, honestly don’t know depends on how your TV behaves with different signals and going analog to digital to analog will probably, sad to say, only make matters worse.